Question

If 2^2.322 = 5 then what does 2^5.322 equal? Explain how you found your answer.

Answer 1

The question says:

'If 2^2.322 = 5 then what does 2^5.322 equal? Explain how you found your answer. '

So we have to use the fact that 2^2.322 = 5, in order to work out what 2^5.322 equals

_______________________________________________

Remember the following indices rule:

a^m times a^n = a^(m+n)

So first we have to use the indice rule to split apart 2^2.322:

`2^(2.322)=2^(2+0.322)=2^2*2^(0.322)=4*2^(0.322)`

Now we can substitute this into the original equation, and work out the approximate value for
`2^(0.322)`:

`2^(2.322) = 5`

`4*2^(0.322)=5`

`2^(0.322)=(5)/(4) =1.25`

Now lets use the indices rule again to split apart 2^5.322:

`2^(5.322) = 2^(5+0.322)=2^5*2^(0.322)= 32*2^(0.322)`

From the previous equation, we worked out that
`2^(0.322) = 1.25`

Therefore:

`2^(5.322) = 32 * 1.25 = 40`

____________________

Answer:

40

Answer 2

40.002

Explanation:

`2^(5.322)` is 2 to the power of 5.322. Only way to find the exact decimal is to calculate in a calculator. When we do so we should get 40.002 as our answer.